Linear Motion Chapters 2 and 3.

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2 Some Terms Motion Vector quantity Scalar quantity DisplacementA change in position over timeVector quantityA factor with magnitude and directionScalar quantityA factor with only magnitudeDisplacementThe change in an object’s positionResultantThe net effect of two or more vectors

3 Motion DiagramsA series of images (or of points) that show the position of a moving object at equal time intervalsSI unit of position is mSI unit of time is sIn order to be useful, we need to establish a coordinate systemEstablish a location to be zero (origin)Establish a direction to be positive (ex. Moving to the right could be positive, moving left would then be negative)

4 Motion ContinuedWe can use these diagrams to create vectors showing the displacement of the moving object from its origin to its ending positionThe direction it points indicates the direction of movement, the length indicates the magnitudeWe indicate the change in a factor by using the Greek letter delta,  (ex.  t is the change in time)2 equations:t = tf – tid = df – diRemember, the signs for the displacements are based on the coordinate system (they could be negative)

5 Graphing MotionYou would plot the dependent variable (displacement) on the y axis and the independent variable (time) on the x axisThe line created represents the location you’d most likely find the object at any particular time (instantaneous location)You could plot more than one line on the same graph (useful if you want to compare the locations of 2 objects moving in the same space)You’d need to use the same coordinate system for bothWhere the lines cross, indicate when they are at the same location

6 VelocityThe rate at which displacement changes with time (a vector quantity)SI unit is m/sCan be found by determining the slope of a line on a position–time graph (rise/run) or using a formula (v = d/ t)The steeper the slope, the faster the object is movingThese both find the average velocity over the whole time period, not the instantaneous velocity

7 Speed versus Velocity They are not the same thingVelocity is in a particular direction, speed isn’tSpeed is a scalar quantity (it cannot be negative), it only indicates magnitude, not directionRemember with our coordinate system, the sign indicates the direction of motionA negative velocity doesn’t mean the object is slowing down, it just means it’s moving in the opposite direction

8 Predicting LocationsCan predict the location of a moving object by continuing the line of the graph out until the desired time pointCan use a variation of the linear graph formulad = vt + div is the average velocity, t is time and di is initial displacement

9 Acceleration The rate at which velocity is changing with timeSI unit is m/s2Occurs because an object speeds up, slows down or changes directionRemember, since velocity is a vector, acceleration is tooA negative acceleration doesn’t indicate slowing down, it indicates the direction of accelerationAn acceleration of zero doesn’t mean the object isn’t moving, just that it isn’t speeding up or slowing down

10 Finding AccelerationCan be done by finding the slope of a velocity-time graph (velocity goes on the y axis, time on the x axis)Can be done using an equation (a = v/ t)As with time and displacement, v = vf - viAs with velocity, these both calculate the average acceleration, not the instantaneous acceleration

11 Using Acceleration to make PredictionsWith a constant acceleration, you can predict a velocity at a given timeYou can use the graph ORvf = vi +a tWith a constant acceleration, you can predict a displacement at a given timeYou can find the area under the velocity-time graph ORdf = di + vitf + 1/2a(tf)2

12 Free Fall Motion of an object due to gravity only (no air resistance)Measure to be 9.8 m/s2 for all objects on Earth (regardless of their mass or size)Remember the sign indicates direction so, we often consider it positive if moving toward the Earth and negative if an object has been thrown upwardAll the same formulas and rules apply, the acceleration will just always be 9.8 m/s2

13 Projectile MotionResults from a combined effect (resultant) of horizontal velocity and vertical velocity (ie gravity)The resultant path is curvedThe horizontal velocity remains constant (a = 0) if no air resistanceThe vertical velocity is changing due to gravity (a = 9.8 m/s2)For any 2 angles of release that add to 90o, the range is the same (horizontal distance traveled)But the bigger angle will remain airborne for longer